How many ordered pairs (a, b) of positive integers satisfy the equation
a \cdot b+63=20 \cdot \operatorname{lcm}(a, b)+12 \cdot \operatorname{gcd}(a, b)
where \operatorname{gcd}(a, b) denotes the greatest common divisor of a and b, and \operatorname{lcm}(a, b) denotes their least common multiple?
Answer Choices
A. 0
B. 2
C. 4
D. 6
E. 8